Gradient Descent for Multi-Objective Optimization to Find a Cohesive Solution for Fenestration Sizes

摘要

While Genetic Algorithm (GA) and Parametric Analysis (PA) have been used to optimize design solutions, they have been barely used to optimize complex design contexts that are multi-objective and multi-variable questions. In this study, I present the results of Gradient Descent (GD) optimization method to optimize skylight sizes by considering all the qualitative and quantitative factors, including daylight availability, glare and energy. The intent was to investigate the feasibility of applying GD for optimizing the average performance using an aggregated metric to represent all the three objectives. The target lighting level was considered 300 lux while Lighting Power Density (LPD) was held constant at 0.8 watt/ sqft for all iterations. GD method as applied to perform an unconstrained multi-objective optimization for the San Francisco climate. GD method results in 10.94% while PA method presents 11% as the inclusive optimal Skylight to Floor Ratio (SFR). Although GD method and PA reasonably agreed on the inclusive optimal SFRs, both methods required different numbers of iterations. Considering SFR resolution of 0.01%, for a Parametric Analysis 10,000 iterations would have been necessary. However, GD method required 5 iterations to find the optimal solution with higher SFR resolution of 0.01%. GD method shows a promisingfuture to apply in building industry to find an optimal solution for a complex design question in a reasonable amount of computing time.